A limiting factor in the efficiency of using nonlinear optical harmonic generation to frequency convert laser radiation comes from phase mismatch between different frequency components of the interacting waves, resulting from material dispersion. This prevents the constructive addition of the nonlinear fields, which oscillate sinusoidally with propagation distance with a period of twice the coherence length (Lcoh), where Lcoh is the distance over which the incident and nonlinear fields accumulate a relative phase of π. A wide range of techniques have been developed over the last decades to compensate for this phase mismatch, allowing the generated nonlinear signal to accumulate constructively over an extended propagation distance (>Lcoh) and hence increase the efficiency of the frequency conversion process. A common procedure is to use crystal birefringence and adjust the polarization of the interacting waves in such a way that the phase velocities are matched.
Another method, known as quasi-phase-matching, is based on the idea that by having a periodic spatial modulation of the linear and/or nonlinear susceptibilities of a nonlinear medium, the relative phase between the interacting waves can be reset and the detrimental effects of phase mismatch on the conversion efficiency are fully or partially corrected, without matching the phase velocities. Periodic poling of ferroelectrics is a common way to achieve this.
To produce the third harmonic of femtosecond laser pulses, for example, to generate near ultraviolet light from near infrared sources, one typically follows a two-step process that generates the second harmonic first, using one crystal, and then mixes the latter with the fundamental, using a second crystal, to obtain radiation at 3ω. Efficiencies typically do not exceed 10%-15%. A more straightforward technique involves using the cubic nonlinearity of isotropic materials through direct third harmonic generation making use of some quasi-phase-matching technique. Several methods have been developed to achieve this, with efficiencies always falling below the two-step method described above.